Galerkin Boundary Element Method for Laplace Equation

Galerkin method based on the variation principle is used to solve differential and integral equations. The boundary problem of Laplace equation is changed into the variational equation which is equivalent to the boundary integral equation. Using linear element, it is solved by Galerkin boundary element method. In computation of stiffness matrix, the exactly integral formula is used in the first order integral expression, The numerical integral formula is used in the second order integral expression. Thus the problem of calculation of double singular integral is carried out. The numerical experiments also prove this method is reliable. The error of Galerkin boundary element is tested with numerical experimentation.     

A NEW BOUNDARY INTEGRAL EQUATION METHOD FOR SOLVING EXTERIOR BOUNDARY VALUE PROBLEMS OF THREE-DIMENSIONAL HELMHOLTZ EQUATION

This paper pressnts a new boundary integral equation method for solving exteri-or boundary value problems of three-dimensional Heimheltz equation by using the multiple reciproc-ity method.Firstly,integral representations of the solution in an exterior domain as well as on itsboundary,which have the peculiarity that integral kernels are infin ite seriesea developed from thenormal fundamental solution of Laplace equation and independent of the wavenumber,are given andproved under the Dirichlet condition.Then,based on the representation of the solution on the bound-ary,boundary integral equations for solving the Dirichlet and the Neumann boundary value prob-lems are obtained,and remarks for some problems concerned with solving these integral equationsnumerically are made.Finally, the advantages of the proposed method,as compared with the conven-tional boundary element methods,are summarized.     

Galerkin Boundary Element Method for Two-dimension Laplace Equation of Neumman Condition

The authors apply the Galenkin variational equation to solve the integral equation with hyper singularity, which can be deduced from the double layer solution for Neumann problem of Laplace equation. The scheme of partial integration in the sense of distributions is introduced to reduce the hyper singularity integral into a weak one with the boundary rotation of unknown function. The numerical implementation with linear boundary elements is presented. The numerical examples illustrate the feasibility and efficiency of the method.     

Galerkin Boundary Element Method for Direct Boundary Integral Eqution for Dirichlet Problem of 2-D Laplace Eqation

The direct boundary integral equation of two-dimensional Laplace equation for Dirichlet problem is(con-sidered).It is deduced by Green's formula and the fundamental solution.The most-used numerical method for solving(direct) boundary integral equation is collocation method,and seldom have been used the Galerkin scheme in this case.The direct boundary integral eqution is changed into the variational eqution.Using linear element,it is solved by Galerkin boundary method.In the variational eqution double integrations shall be carried out.The paper presents the analytical formula to calculate the inner integration and the Gaussian quadrature is used for the outer integration. The numerical experimentation proved thefaesibility and the efficiency.     

Boundary Element Methods with Overlapping Domain Decomposition for Parabolic Problem

Boundary element method is a numerical method for solving partial differential equations. There are several formulations of boundary element method (BEM) applied to solve a parabolic differential equation.The approach,which employs time- dependent fundamental solution,allows longer time steps in time integration than other approaches,and this can cut down on time for computer implementation with high precision.Domain decomposition method,which decompose the domain that a given problem is to be solved into subdomains,has the advantages of reducing the large problem into smaller ones and reducing the complex problem into simpler ones,and allows parallel computing.An overlapping domain decomposition method is applied combining a boundary element formulation with time-dependent fundamental solution to solve a diffusion equation. Firstly, by domain decomposition, the problem divided into two problems on subdomains, and then the initial-Boundary problems are solved by boundry element method on each subdomain.Some numerical examples are presented to illustrate feasibility and efficiency of the method. The numerical experiments show that the convergence rate of the method is dependent with the overlapping degree of the subdomains.     

Positive Solutions of a Kind of Special Nonlinear Neumann Boundary Value Problems

The purpose of this paper is to consider a kind of special nonlinear Neumann boundary value problems. The kind of boundary value problems has not Green function. Using suitable transformation,we can change these problems to general Neumann boundary value problems. By applying integral equation and degree theory on cone,the existence of n positive solutions is proved for the kind of problems,where n is an arbitrary natural number.     

Analytic Method for the Free Vibration of Plane Frame Structure

The analytic method for the free vibration of plane frame structure is presented. It is achieved by transforming the general eigenvalue problem of natural frequency and vibration mode of continuously distributed property system into typical boundary value problem of ordinary differential equation (ODE). A series of ODE, corresponding to the general eigenvalue problem, is formed, and then is solved by an general ordinary differential equation solver-COLSYS. Each component of a frame structure is regarded as an element in the analytic method. This makes it more efficient than that of finite element method which needs to increase elements to get the value of high-class natural frequency and vibration mode accurately. Some applications of the method show that it can solve the free bending vibration of plane-frame structure with various types of displacement constraint. The result indicates that this method is precise and efficient.     

Quadrature Methods and Their Extrapolations for Solving Boundary Integral Equations of Steady Navier-Stokes Problems

This paper presents an iteration method of solving non linear boundary integral equations (BIE) of the plane Navier Stokes problem,which each step of the iteration is to solve a linear BIE of nonhomogeneous Stokes problem. Using the quadrature methods of [1],we give a new algorithm with a high order accuracy.The algorithm not only saves work,but also the accuracy can be improved by Richardson extrapolation.     

水稻边际优势利用栽培增产的生态原因研究

对大小垄栽培群体和30cm等行距栽培群体不同层次的光照强度、群体行间温、湿度等生态因子及每穴穗数、每穗实粒数和单穴生产力三个产量性状和不同分蘖时期每穴茎数的边际效应指数进行了研究。结果表明,大小垄栽培群体下部的光照强度和透光率显著增加,行间温、湿度降低,使群体内部的光、温条件得到改善。每穴穗数、每穗实粒数和单穴生产力及不同分蘖时期每穴茎数的边际效应指数降低,说明实行大小垄种植后,群体内部的长势与边行的差距缩小,群体内部个体的生长优势得到发挥,达到了利用边际优势增产的目的。     

水稻边际优势利用栽培增产的生态原因分析

对大小垄栽培群体和30cm等行距栽培群体不同层次的光照强度、群体行间温、湿度等生态因子及每穴穗数、每穗实粒数和单穴生产力三个产量性状和不同分蘖时期每穴茎数的边际效应指数进行了研究。结果表明,大小垄栽培群体下部的光照强度和透光率显著增加,行间温、湿度降低,使群体内部的光、温条件得到改善。每穴穗数、每穗实粒数和单穴生产力及不同分蘖时期每穴茎数的边际效应指数降低,说明实行大小垄种植后,群体内部的长势与边行的差距缩小,群体内部个体的生长优势得到发挥,达到了利用边际优势增产的目的。     

The Research about Operating State of Enterprise in Exessive Indebtedness and the Boundary of Pressed for Funds

It analyzes the operating state of enterprise in exessive indebtedness by the methods of statistical and break even analysis; and it analyzes the boundary of pressed for funds by the methods of assets structure and business effective analysis.Submit the train of thought for scientific research in enterprise operating with debts.     

用数学模型方法选择人工薪炭林树种

人工薪炭林是当前人工林建设中的重要林种,它与人民生活息息相关。笔者拟通过寻找区域内各主要适生薪炭林树种,对其采样的重量和样本燃烧的热值建立多元回归方程的数学模型的思想,从而找出燃烧热值最高的一种或者几种优势薪炭林树种,为科学准确选择合理的人工薪炭林树种提供理论依据。     

An Analysis of Thick Plates underIn-plane and Transversal Loadings by the BEM

In accordance with the behaviours of thick plates under the in-plane and transversal loadings,and introducing the concept of equivalent load, the coupled equations for the problem have been deduced with the theory of BEM in this paper.Thus a new method is presented for solving the problems of interaction of superstructure and foundation and subsoil,as well as for the problems of the thick plates under the complicated loadings.     

A Three Dimensional Torso Model for the Numerical Simulation of ECG--Forward Problem of ECG(1)

In this paper,a numerical model of a three dimensional human torso has been presented.In this model,the torso part including anisotropic muscle layers has been discretized by means of the finite element method(FEM).The rest of torso have been divided into the surface elements by the boundary element method(BEM).This discretized model can be used in the field such as the forward problem and the inverse problem of the electrocardiogram(ECG).     

几种水生植物组合对畜禽产品加工废水净化效果的研究

菖蒲对废水具有较好的净化效果,水葱、酸模、鸢尾对废水也有一定的净化效果,笔者将寻找一种挺水植物与菖蒲的组合对畜禽产品废水具有更好的净化效果,从而在生产上推广应用。笔者选择菖蒲与水葱、酸模、鸢尾组合的3个试验组,只有洗沙的无植物空白试验作为对照组,测定试验前后的9个指标。试验结果表明：对畜禽产品加工废水处理过程中,所选3种组合生长良好并表现出较好的三氮、氮磷及COD净化效果。其中,菖蒲+鸢尾对NH3-N、NO2-N的净化效果最好,去除率分别为90.35%、51.91%;菖蒲+酸模对NO3-N的净化效果最好,去除率为14.24%。相对空白对照的去除率,菖蒲+水葱的总磷净化性能最好,提高4%;菖蒲+酸模组、菖蒲+鸢尾组COD净化性能最好,分别提高0.36%、0.29%。     

低磷胁迫下水稻不同品种根系有机酸分泌的差异

以4个对低磷反应不同的典型水稻品种（系）为材料，对其在低磷胁迫下根系有机酸分泌这一根系生理特性进行了比较研究。结果表明，低磷胁迫能促使水稻根系分泌更多的有机酸，这在耐低磷品种中表现尤为明显。     

水肥耦合对紫色土中小麦肥料减施效应的影响

为了认识水肥耦合对紫色土中小麦的影响特征及肥料减施效应,在四川盐亭县青峰村和四川盐亭农田生态系统国家野外科学观测研究站的石灰性紫色土上,于2018年10月至2020年5月,用小区和盆栽试验等方法,观测不同水肥耦合处理对小麦和土壤主要属性的影响。结果表明,水肥耦合对小麦生长和籽粒产量有明显的促进效应,浇水到田间持水量的80%左右时,其促进效应最大;肥料用量减少10%～20%,不会造成小麦的明显减产;水肥耦合主要提高了土壤养分有效性和土壤酶的活性,因而有明显的促进效应。水肥耦合是紫色土区减肥增效的一种有效措施,从而能有效防治区域的面源污染。     

专业学位研究生联合培养实践基地建设探讨

研究生联合培养基地是实现专业学位研究生创新实践能力培养的重要保障。以河南工业大学粮油食品学院为例,论述了食品工程专业学位研究生联合培养基地建设的必要性及成效,同时分析了实践基地建设目前存在的问题,并从建设数量、培养模式和考核机制等方面提出了相应的对策。     

宝鸡市城郊农田土壤重金属污染风险评估

为了揭示城市化和工业化等人为活动对土壤环境质量的影响,选择宝鸡市城郊结合部为研究区域,对土壤样品Cu、Zn、Pb、Cd和Cr 等5种重金属进行了测定;采用单因子污染指数、综合污染指数法、地积累指数、内梅罗指数和H?kanson潜在生态危害指数对土壤重金属污染状况进行评价,同时运用潜在生态危害指数法分析研究了土壤重金属的潜在生态风险程度。结果表明：研究区域土壤中的5种重金属中除Cd的平均累计含量已超过国家土壤环境质量标准GB15618-2008中的二级标准外,其它4种重金属元素的平均累计含量均未超过国家二级标准;内梅罗综合评价结果表明宝鸡城郊农田土壤大多数采样点重金属污染处于尚清洁水平,S3和S5点处轻度污染,S7点中度污染,S6点为重污染;地积累指数评价结果,5种重金属的污染顺序为Cd≥Cu≥Pb≥Zn≥Cr;5种重金属中Cd是生态风险最大,单个潜在生态危害程度为Cd＞Cu≥Pb≥Cr≥Zn;综合潜在生态危害评价显示,在S6和S7处综合为强生态危害,S3、S5和S10处中等生态危害,其余采样点处为轻微生态危害。源解析研究表明研究区域土壤中的Pb、Cu、Cr和Zn来为同一污染源,而Cd为另外某一污染源。